A Simple Physics Question?

I was wondering about gravity and weight? I apologize if this question seems elementary to you all, so please forgive me as i am not a scientist. If gravity acts equally on all objects regardless of size or mass, (ie. drop a bowling ball or a penny, they both fall at the same speed right?) then why do they have different weights when at rest on the ground? If mass and gravity have nothing to do with one another, then why do larger planets have stronger gravity? Or for that matter, why is the sun's gravitational field so much larger than ours? thnx.

When someone says that gravity 'acts the same' on all objects, what they mean is that the acceleration is the same. However, the force is defined as mass times acceleration. Weight is a synonym for force, so therefore varying masses produce a varying force. That's the mathematical reason, anyways. I guess I could get into how mass could also be defined in how much it resists changes in inertia, but oh well, someone else will!

Gravity is dependent on mass. Force = (G)*M1*M2/(r)^2 (Newton's gravitational law)
where G = is the gravitational constant, M1 and M2 are two masses, and r is the distance between the center of mass of both

Let M1 = PlanetMass. Therefore, M2 = Mass of object on planet. The force on M2 is equal to M2*a, where a is the acceleration ('gravity') due to the planet mass.

I guess i better explain 'weight' in a more intuitive manner. Let's say we have two shopping carts, one which is laden with groceries and the other which is empty. Which one will it be easier to accelerate in a certain amount of time to a certain velocity. The empty one of course! The heavy cart can have the same acceleration but it will require a greater force to do it. Therefore, the heavy cart has more 'mass' than the lighter cart. Mass can be defined as the resistance to change in inertia. Inertia is simply the object staying in motion. Is it not harder to stop the heavy cart once its moving than stopping the lighter cart? Since the heavy cart is harder to stop at the same speed as the lighter cart, it has more inertia and thus more mass than the lighter cart.

Now, I've demonstrated intuitively that the more mass the object has the more force (i.e. 'weight') it is required to accelerate. Since the planet accelerates objects at the same value, it will take more force to accelerate heavier objects than lighter ones. Thus, the heavier object 'weighs' more (has more force exerted on it).

Good responses, Durato.
One thing I would like to add is that the acceleration of gravity is only equal for vastly different objects if they're in vacuum (or very thin air). A 50-gram ball bearing will outrace a 100-kilogram guy with a parachute every time in our atmosphere.

i have another quick question regarding einsteinian space-time geometry. einstein's idea of space-time is analogous to a flat sheet spread out with the objects in the universe creating small or large dips in the sheet, right? and this is what causes a gravity well, to an extent in the general vicinity of a planetoid, right?

ok, this is what i'm wondering - the sheet analogy is only 2-dimensional? are the dips (in space-time) occuring at every angle to the objects? for example, is space warped not just underneath but above as well as at all angles to the object? so the planetoid would create in effect, an almost entire inward limited collapse of space-time? thnx again

Good responses, Durato.
One thing I would like to add is that the acceleration of gravity is only equal for vastly different objects if they're in vacuum (or very thin air). A 50-gram ball bearing will outrace a 100-kilogram guy with a parachute every time in our atmosphere.

Careful there Danger. The acceleration due to gravity is essentially constant on Earth regardless of whether it is in a vacuum or not. The issue you are talking about is the resisting drag force created by the atmosphere. That is a completely different issue.

Okay, I'm a bit confused on that, Fred. While the gravity is trying to accelerate everything equally, doesn't the drag in fact decrease the actual acceleration?
(Maybe I'm using the wrong terminology.)

i have another quick question regarding einsteinian space-time geometry. einstein's idea of space-time is analogous to a flat sheet spread out with the objects in the universe creating small or large dips in the sheet, right? and this is what causes a gravity well, to an extent in the general vicinity of a planetoid, right?

ok, this is what i'm wondering - the sheet analogy is only 2-dimensional? are the dips (in space-time) occuring at every angle to the objects? for example, is space warped not just underneath but above as well as at all angles to the object? so the planetoid would create in effect, an almost entire inward limited collapse of space-time? thnx again

Absolutely. The example of a rubber sheet is quite a bad one actually as it indeed does only show a 2D world. The existence of mass causes a spatially 3dimensional warp in spacetime whose force is described by F=G*m1*m2/r (Newtonian) where F is equivalent in any direction with a constant r and constant masses.

It is quite hard to picture a 3D example of gravity warped spacetime, and thats why the popular model is the 2D sheet one. For what it is worth if you would like to try, when I attempt to picture what gravity warped space looks like I first picture space as a 3 dimensional grid with x,y, and z. Then I try and picture what it would look like if a point mass was introduced and all the lines in the grid system were bent so that an object traveling trough this grid would experience a circular motion towards the point mass.

Obviously this is only a conceptual model as spacetime cannot be seen directly.

Okay, I'm a bit confused on that, Fred. While the gravity is trying to accelerate everything equally, doesn't the drag in fact decrease the actual acceleration?
(Maybe I'm using the wrong terminology.)

No. Gravitational acceleration only varies at different elevations on Earth. It is essentially constant as Fred pointed out.

You are thinking about the terminal velocity of an object which is dependent on the drag. Hence, if two different objects are placed in a vacuum, the fall at the same rate.

Thnx Rob! I always wondered about that, it makes sense, i always thought so. And i can actually visualize it without the need for picture or graph. This gives me a new found appreciation for einsteinian space-time geometry! You add this to the idea that a spinning planetoid is causing a frame dragging affect on space-time as well, and that makes it even wilder! Thnx again. Now i have a million ideas going through my mind regarding the underlying nature of the fabric of space-time itself and why these warps play out as gravity at all?

It is quite hard to picture a 3D example of gravity warped spacetime, and thats why the popular model is the 2D sheet one. For what it is worth if you would like to try, when I attempt to picture what gravity warped space looks like I first picture space as a 3 dimensional grid with x,y, and z. Then I try and picture what it would look like if a point mass was introduced and all the lines in the grid system were bent so that an object traveling trough this grid would experience a circular motion towards the point mass.

there was a screensaver in win98 which sorta did what you just described. i think they called it blackhole.. you could change some parameters like its radius and all, it seemed pretty cool at the time..

No. Gravitational acceleration only varies at different elevations on Earth. It is essentially constant as Fred pointed out.

I suspect that stewartcs misinterpreted what was said. I interpreted as: "While g is equal for both objects, doesn't the drag decrease the net rate of change in velocity?" Yes, dv/dt ~ g - (b/m)v.

Alternative example: "One thing I would like to add is that the equal acceleration of gravity is only visually apparent for vastly different objects if there are no other dissimilar forces interfering such as air resistance..."

To add on to everyone elses responses, the sensation of weight is given by whats known as an objects normal force. if it is just a person standing on earth it is m*g. As newton pointed out, for every action there is an equal an opposite reaction. So, you push down on earth, earth pushes up on you with the same force. An object will have the same mass on earth as it would in a vacuum, the weight however, would change due to the lack of a normal force in a vacuum.